They wish. China's not a DPRK-style absolutist state just because they call themselves Commies. The PRC has an elaborate, confused power structure with lots of rivalries and competing interests. The PLA (and PLAN and PLAAF) functions more like a combination of labor union, coporation and political party than the "politically neutral, obedient to civilian leadership professionals" military we know and love. Biggest difference is that they're good at keeping internal debate seriously internal, and the populace doesn't expect to have a say in whatever the State decides to do. China's been an authoritarian state damn near literally since time began.
Anyway...you can declare that you're building a sexy new Navy, even build one on demand, but it's a whole 'nother thing to make it work and know what to do with it. Especially when it comes to carrier flight ops. When the Chinese first announced they were buying Varyag, some wise fellow (I forget who, ADM Jay Johnson maybe), said something to the effect of, 'they can have at it; it took us 50 years to learn how to do it without killing ourselves'.